Pith Number

pith:LY7APWF2

pith:2011:LY7APWF2U5ECZNG6PTE2BD5VTG

not attested not anchored not stored refs pending

Control of the isoperimetric deficit by the Willmore deficit

Matthias R\"oger, Reiner Sch\"atzle

arxiv:1106.6213 v1 · 2011-06-30 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LY7APWF2U5ECZNG6PTE2BD5VTG}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:19:03.747256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e3e07d8baa7482cb4de7cc9a08fb599b559a92116422e6330deb62cd39e694e

Aliases

arxiv: 1106.6213 · arxiv_version: 1106.6213v1 · doi: 10.48550/arxiv.1106.6213 · pith_short_12: LY7APWF2U5EC · pith_short_16: LY7APWF2U5ECZNG6 · pith_short_8: LY7APWF2

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LY7APWF2U5ECZNG6PTE2BD5VTG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 5e3e07d8baa7482cb4de7cc9a08fb599b559a92116422e6330deb62cd39e694e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "560f2d50cee9f1971e8f6c4a5007dd29dd3d3f6ea233505827b07e84b7a30be5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-06-30T12:58:11Z",
    "title_canon_sha256": "e213cb7ce1c98efe4751ab19b7ba5b3f601ae68ecab034db9b4ae03f7fc241a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.6213",
    "kind": "arxiv",
    "version": 1
  }
}